Why Can't You Add Fields Component-Wise for a Dipole?

[Saladsamurai]

[SOLVED] Electric Field due to a Dipole

Homework Statement

The figure shows two charged particles on an x axis: -q=-3.20(10^{-19})C and q=q=3.20(10^{-19})C. They are both a horizontal distance of 3 m from the y axis. What are the magnitude and direction of the net electric field produced at P at y=4 m?

Okay. So I know I can use the Dipole equation for this, but I had originally tried placing a test charge at P and adding the fields component wise.

I got the wrong answer and I was just wondering why you cannot take this approach?

This is what I had tried:
E_{px}=\sum E_x=k[\frac{-|q_1|-|q_2|}{d^2}](\frac{3}{5})=-3.836(10^{-10})

And
E_{py}=\sum E_y=k[\frac{-|q_1|+|q_2|}{d^2}](\frac{4}{5})=0

 

[Saladsamurai]

Nevermind. This works! I was using the wrong d!